Date: Feb 11, 2013 4:19 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots
In article

<59abfe03-8386-4d06-8f54-acfbf19a50d0@x15g2000vbj.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 11 Feb., 16:40, William Hughes <wpihug...@gmail.com> wrote:

> > On Feb 11, 4:03 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> >

> > > On 11 Feb., 11:55, William Hughes <wpihug...@gmail.com> wrote:

> >

> > > > On Feb 11, 8:50 am, WM <mueck...@rz.fh-augsburg.de> wrote:

> >

> > > > > There exists a natural number m such that d is line number m is false.

> >

> > > Yes so, alas not quite correct if d is assumed to "exist".

> >

> > > If d is assumed to exist, we have

> >

> > > 1) We cannot *find* a natural number m such that d is the m-th line of

> > > the list.

> >

> > According to you

> >

> > if L is a potentially infinite list, and d is

> > the potentially infinite diagonal

> >

> > if for every natural number n, d is not the nth

> > line of L then

> >

> > *There does not exist* a natural number m such that

> > d is the mth line of L

> >

> > Do you wish to withdraw this claim?

>

> No. This claim is obviously correct.

>

> Only *if the complete existence of the not completely existing

> diagonal d is assumed*, it would be necessary to have it in the list

> and (since every line of the list contains everything that is

> contained by its predecessors) to have it in a line of the list. But

> obviously a potentially infinite diagonal does not exist completely

> (as the potentially infinite list does not exist completely).

>

> So why should anything be withdrawn?

The notion of potential infiniteness should be withdrawn as it is

incompatible with the notion of "set".

One cannot have a set whose membership is only potentially determined.

In all standard set theories there is a set which contains {} as a

member and which for each of its members, m, also contains (m union {m}).

Since this is apparently not the case in WMytheology , then no set

theory in WMytheology is compatible with standard mathematics , and thus

WMytheology irreleveant to standard mathematics.

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